GREEDYKLS |
Greedy Regularized Kernel Least Squares.
Synopsis:
model = greedykls(X)
model = greedykls(X,options)
Description:
This function approximates input vectors X in the feature
space using GREEDYKPCA. Then the regularized least squares
are applied on the approximated data.
See help of KLS for more info about regularize least squares.
See help of GREEDYKPCA for more info on approximation of data
in the feature space.
Input:
X [dim x num_data] Input column vectors.
y [num_data x 1] Output values.
options [struct] Control parameters:
.ker [string] Kernel identifier. See HELP KERNEL for more info.
.arg [1 x narg] Kernel argument.
.m [1x1] Maximal number of base vectors (Default m=0.25*num_data).
.p [1x1] Depth of search for the best basis vector (Default p=m).
.mserr [1x1] Desired mean squared reconstruction errors of approximation.
.maxerr [1x1] Desired maximal reconstruction error of approximation.
See 'help greedyappx' for more info about the stopping conditions.
.verb [1x1] If 1 then some info is displayed (default 0).
Output:
model [struct] Kernel projection:
.Alpha [nsv x new_dim] Multipliers defining kernel projection.
.sv.X [dim x num_data] Selected subset of the training vectors.
.nsv [1x1] Number of basis vectors.
.kercnt [1x1] Number of kernel evaluations.
.MaxErr [1 x nsv] Maximal reconstruction error for corresponding
number of base vectors.
.MsErr [1 x nsv] Mean square reconstruction error for corresponding
number of base vectors.
Example:
x = [0:0.05:2*pi]; y = sin(x) + 0.1*randn(size(x));
model = greedykls(x,y(:),struct('ker','rbf','arg',1,'lambda',0.001));
y_est = kernelproj(x,model);
figure; hold on;
plot(x,y,'+k'); plot(x,y_est,'b');
plot(x,sin(x),'r'); plot(x(model.sv.inx),y(model.sv.inx),'ob');
See also
KERNELPROJ, KPCA, GREEDYKPCA.
About: Statistical Pattern Recognition Toolbox
(C) 1999-2005, Written by Vojtech Franc and Vaclav Hlavac
Czech Technical University Prague
Faculty of Electrical Engineering
Center for Machine Perception
Modifications:
01-mar-2005, VF
22-feb-2005, VF